Brooklyn Borough President Eric Adams shocked some local business and community leaders at a Borough Hall meet-and-greet recently, hitting them up for cash to fund pet projects — with the money to be funneled through a nonprofit that doesn’t even exist.

“If this is how Eric is starting out, the borough is really in trouble,” said a business leader who attended Thursday’s event.

The former state senator and retired NYPD cop, who took the borough’s reins in January, had his staff distribute fliers and “Partner/Sponsor” application forms — copies of which were obtained by The Post — claiming the money would go to his “affiliated nonprofit,” called One Brooklyn, to fund various cultural events throughout the year.

“Collaboration between public, private and nonprofit sectors is essential in addressing our societal needs and solving community problems,” the One Brooklyn form said.

The paperwork bears an official-looking insignia that includes the Seal of the City of Brooklyn over a ribbon bearing the words “One Brooklyn.” But the state Division of Corporations said it has no record of any such nonprofit or any other entity named One Brooklyn.

Although Adams attended the event, he had one of his top staffers, Valerie Oliver-Durrah, do most of the fund-raising appeal, sources said.

The lapse could leave Adams and even his staffers open to “potential fraud charges,” according to a nonprofit legal expert who spoke to The Post on the condition of anonymity.

“You can’t raise money for a charity that doesn’t exist,” the expert said. “The question is: Whose bank account would receive the donations if there’s no such organization?”

Even if One Brooklyn does exist, Adams would need the blessing of the Conflicts of Interest Board before hitting anyone up for money in a government building, officials said.

Asked about the fund-raising effort, Adams acknowledged not having set up the nonprofit. He told The Post in an e-mail that his “office is working closely with the Conflicts of Interest Board and other relevant entities to ensure that public-private partnerships are pursued in the proper manner.”

But the Conflicts Board said that Adams, as of Monday, hadn’t applied for any such approval. Those found guilty of violating city conflict-of-interest laws face fines of up to $25,000 per offense.

“I look forward to expanding this robust vision of public-private synergy across our borough, just as my colleagues in city government are pursuing for their constituencies,” Adams said.

Thursday’s meet-and-greet attendees, including representatives from Con Edison and National Grid, were given a list of dozens of events seeking sponsorship, such as one Latino Heritage Day and a Thanksgiving Turkey Drive.

It also listed at least 20 events claiming to already have various sponsors locked in, including three that already took place and a March 18-21 event called “McDonald’s HS Basketball Honors” that is supposed to be taking place at Barclays Center under the sponsorship of Knicks star Carmelo Anthony.

A Barclays Center official said Monday it has no such event on the schedule.